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Anyway, as told to me, the illegitimate child was sent to an orphanage in London, and my mother said that the Graham surname came from the owner of the orphan's home, though I haven't been able to find a Graham orphanage in the UK at the turn of the century, never mind one in London. 

Although I'm confident of having found his birth in London at the St Pancras poor house, and his army record at the age of 24, I've found nothing of his life in between and still consider the option of his having been raised in an orphanage as reported by my mother to be quite plausible.  I had not found any orphanages run by anyone of the surname Graham, but on reading "Children's Homes: A History of Institutional Care for Britain's Young", in the chapter on Thomas Barnardo, I found:
'The opening of his Ever Open Door in Edinburgh was viewed with antipathy in Roman Catholic quarters of the city, and the London-based Catholic Herald published a story alleging cruelty and neglect by James and Janet Graham, the managers of the home. Although the Grahams successfully sued the paper’s publisher, Charles Diamond MP, Barnardo decided to withdraw from Edinburgh and the home was closed shortly afterwards.'

Alfred and Eliza went to Australia soon after marrying.  Children born in Victoria - John Charles (1884), Henry William (1887), Jessie (1891).

https://my.rio.bdm.vic.gov.au/

Debra 

Thank you.  That does look like a fairly definitive 'no'.

Back again, we've been busy for a couple of days.  Here's the big news: we found and got a copy of the official birth registration, and it pretty much confirms that we're on the right track.  We have the definitive birth date of 2 Feb 1891 in (St) Pancras workhouse, and the new information of the mother, Louisa Harris, being "a domestic servant of 111 Kings Cross Rd, (St) Pancras."  My grandfather name is given as "Thomas" with no father's name being present.  I realise that the probability of an unmarried mother being a domestic servant is relatively high but I don't think it's a Type I error to see the listed occupation as evidence contributing to confirmation of the oral family history.
 
Unfortunately no D.O.B. given for Louisa Harris but we'll get there eventually, perhaps with the DNA help.

The birth date suggests a conception date late April/early May 1890.

You say you 100s of DNA matches to sort thru
But there are ways of narrowing down search parameters using the filters
For example  use location search + colour code all matches with London connection
You can also have a colour code for particular surnames found on trees
The option of tree owners surname can be useful
But I prefer surname found on tree
Look at tree of highest match + try the filter search with surnames of each of their great grandparents
https://www.rootschat.com/forum/index.php?topic=862688.0

I'm often finding new features at Ancestry.com that I wasn't aware of, so I'm not going to say that doing the above is impossible, but I have no idea how to do it yet.  There's 10,000+ DNA matches, but less than 200 show up on the map.  I don't see any way to search by location of people in the tree of those matches.  The only search by name is a blanket search of a given surname against anyone in the tree of a DNA match or against the surname of a DNA match themselves.

Something complex like finding a DNA match to someone who has a great-anything grandparent who lived or was born/died in a specific town seems impossible.  I think Ancestry would have to allow direct access to SQL queries to do that, but as far as I can see there's no API for the public.  (I programmed SQL databases for about 3 years.  I'ld be able to use direct access if it were available.)

And repeatedly the most interesting possible links turn out to be behind private trees, and our success rate at asking for access has been dismal. We've made ours open but people seem unwilling to reciprocate.

I'ld love to try the things you're suggesting but either you're used to a different DNA service with more useful search options, or more likely, my difficulties are because I still have a long way to go to learn the tricks to use Ancestry's one because they're not obvious to me -  for instance, I did just in the last 10 minutes discover the "Shared Matches" tool and that has opened up the possibility of a whole lot of new insights.  So I'm getting there slowly...

G

Some significant new information!  In going through Thomas Graham's army papers we found the page below where he declared his next-of-kin.

I'm not 100% sure of the Christian name - It looks like Hannah but at a stretch could be Marrian or Marriam although most variants of those have only 1 'r' so I've been concentrating on Hannah. But the surname and the word 'Mother' is clear.  It looks like Mrs Hannah Graham Barrett, with the Graham scored out.  There's also the word "man's" to the right but I cannot see "man's"-what? - maybe Man's address?

The address is 310 Hornsey Road, Holloway, London.  It looks like he gave the info in 1914.

This could be his adoptive mother!

I tried searching in the 1911 census but I don't have a way to search by street address to see who lives there.  I've spent most of this evening searching but haven't yet found a plausible match for Hannah Barrett, Hannah Graham, or Hannah Graham Barrett. 

The scoring out of the word Graham in her name is either because the person transcribing the information expected Thomas Graham's mother to also have the Graham surname, but she didn't and he got ahead of himself copying down what Thomas said; or she *was* Hannah Graham or Hannah Graham Barrett but her husband had died recently and she was reverting to her maiden name.  Or something else entirely different as to which I cannot guess.

Do you know of any way to pin this person down or the occupants of the given address in 1914? Especially if there was a proper legal adoption.

Thanks,

Graham